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D-brane non-perturbative effects and geometric deformations

Anatoly Dymarsky, Luca Martucci

Abstract

We study how non-perturbative dynamics on D-branes affects the ten-dimensional geometry. We show that a gaugino condensate changes the complex and the symplectic structures of the original manifold by deforming the supersymmetry conditions. The cases of D5, D6 and D7-branes are discussed in detail. In the latter case we find the explicit form of the resulting back-reacted background at linear order in the gaugino condensate.

D-brane non-perturbative effects and geometric deformations

Abstract

We study how non-perturbative dynamics on D-branes affects the ten-dimensional geometry. We show that a gaugino condensate changes the complex and the symplectic structures of the original manifold by deforming the supersymmetry conditions. The cases of D5, D6 and D7-branes are discussed in detail. In the latter case we find the explicit form of the resulting back-reacted background at linear order in the gaugino condensate.

Paper Structure

This paper contains 26 sections, 169 equations.

Table of Contents

  1. Introduction
  2. Geometric deformations from condensing D5-branes
  3. The classical background
  4. Gaugino condensation and supersymmetry
  5. The analogy with the heterotic M-theory case
  6. Compactification and tadpole supersymmetry breaking
  7. Relation with holographic geometric transitions
  8. A comment on the case of fractional D3-branes
  9. The mirror conifold picture: condensing D6-branes
  10. Condensing D7-branes and generalized complex deformations
  11. Intermezzo I: ${\cal N}=1$ vacua and generalized geometry
  12. Unperturbed backgrounds with D7-branes
  13. Gaugino condensation and generalized geometry
  14. Intermezzo II: $\langle S\rangle$-deformed condition for ${\cal Z}$, in general
  15. Back to D7-branes with $\langle S\rangle\neq 0$
  16. ...and 11 more sections